biogeme.expressions.log_sampled_cross_nested module

Arithmetic expressions accepted by Biogeme: sampled cross-nested logit.

class biogeme.expressions.log_sampled_cross_nested.LogSampleCrossNested(utilities, log_probabilities, alphas, mev_utilities, mev_weights, mev_alphas, nests, choice=0)

Bases: Expression

Log probability for a sampled cross-nested logit model.

This expression is designed for the sampling-of-alternatives framework.

It represents the same expression currently generated by GenerateModel.get_cross_nested_logit:

\[\log P(0 \mid S) = K_0 - \log \sum_{i \in S} \exp(K_i),\]

where

\[K_i = V_i - \omega_i + \log G_i,\]

and

\[G_i = \sum_m \alpha_{im}^{\mu_m} \exp((\mu_m - 1) V_i) B_m^{1/\mu_m - 1},\]

with

\[B_m = \sum_{j \in S^{MEV}} w_j \alpha_{jm}^{\mu_m} \exp(\mu_m V_j).\]

The expression avoids constructing a large tree of ConditionalSum, ConditionalTermTuple, exp, logzero, and loglogit expressions.

Parameters:

• utilities (dict[int, ExpressionOrNumeric])

• log_probabilities (dict[int, ExpressionOrNumeric])

• alphas (dict[str, dict[int, ExpressionOrNumeric]])

• mev_utilities (dict[int, ExpressionOrNumeric])

• mev_weights (dict[int, ExpressionOrNumeric])

• mev_alphas (dict[str, dict[int, ExpressionOrNumeric]])

• nests (NestsForCrossNestedLogit | OldNestsForCrossNestedLogit)

• choice (ExpressionOrNumeric)

deep_flat_copy()

Deep flat copy.

Return type:

LogSampleCrossNested

get_value()

Evaluate the sampled cross-nested logit log probability using NumPy.

Return type:

float

logit_choice_avail()

Return availability structures appearing in this expression.

Return type:

list[LogitTuple]

recursive_construct_jax_function(numerically_safe)

Generate a compact JAX function for sampled cross-nested logit.

Return type:

Callable[[Array, Array, Array, Array], Array]

Parameters:

numerically_safe (bool)